Okay I'ma make it simple for you. So listen closely
Blades are like people, and when a human bonds with them then they have a human like body, also having a core crystal. But it doesn't always have to be a human it can be like a polar bear or something. Anyways they're BLADES a d Mythra is the Aegis which is one of the super powerful blades, a Sword. She suppressed herself and turned into Pyra because she caused havoc with her powers on accident. So Pyra is Mythra and Mythra is the Aegis and the Aegis is a sword. Get it now?
Also at the end of the game Pyra and Mythra become separate beings so yippee!!!